Given enough graphical data, could you train an AI to plot a polynomial graph based on the input conditions?
Yes this is possible, using any machine learning approach that supports regression. You have two main approaches:


Input $h$ the height of the drop, multiple outputs, one per time offset that you want to plot. Each individual output calculates the predicted force at a specific offset time.
Inputs $h$ the height of the drop and $t$ a time offset, one output. The single output calculates the predicted force due to given height and at given time.


The main thing to bear in mind is that statistical learning techniques typically do not generate physics-like models. Test inputs close to training examples should generate reasonable graphs that interpolate between those from training data. Test inputs far away from the training examples (e.g. you train on data of drops from 60m to 140m, but use an input of 10m or 200m) will likely generate wildly incorrect outputs. The main exception to this is if your ML model includes some good guesses at the underlying physics model, in which case it is possible that a regression algorithm will tune the parameters of that model plus filter out terms that should not be part of the model, resulting in a system that extrapolates much better. That is very unlikely happen by chance, it requires up-front design.